Non-Linear Indentation Law for Lightweight Sandwich Beam

Abstract

Indentation law is the relationship between force and deflection under the load on a sandwich beam in a fully backed state (on rigid ground). In the classical method, the Winkler model, which is based on analysing a beam on elastic foundation, is used for verifying the indentation law and for measuring core compression yielding load. This load is assumed to be the same as the one in the three-point bending (3PB) state. The typical formula of indentation is F= Kα n, where K and n are determined by an indentation test and α is the sandwich compression. In the present article, the sandwich beam is analysed by the higher order sandwich panel theory (HOSPT), and the indentation law is determined for fully backed and 3PB states separately. The effect of contact width on non-linearity of the indentation law is investigated, and the contact width is determined for cylindrical indentors. Foam, laminate, and sandwich beam contact pressure profiles are presented, and the indentation law is obtained in accordance to the radius of the indentor and contact width. It presents an analytical solution for the factors K and n in the indentation problem for simply supported and fully backed states. It is shown that the core compression in the 3PB state is lower than fully backed indentation. However, the classical theory predicts lower value for it than experimental value. It is shown that K increases as the indentor radius increases in the indentation law. Results are compared with the Winkler foundation method, ANSYS FEM software, and the previous article. Good agreements are found between HOSPT, ANSYS, and the previous work.